Emissivity and the Fate of Pluto's Atmosphere

Icarus 141, 299–306 (1999) Article ID icar.1999.6169, available online at http://www.idealibrary.com on

Emissivity and the Fate of Pluto’s Atmosphere

J. A. Stansberry1 Lowell Observatory, 1400 West Mars Hill Road, Flagstaff, Arizona 86001 E-mail: [email protected]

and

R. V. Yelle2 Center for Space Physics, Boston University, Boston, Massachusetts 02215

Received July 30, 1998; revised February 19, 1999

out that the vapor pressure of such an atmosphere would un- We present a simplified model for seasonal changes in Pluto’s dergo large pressure changes as the temperature of the ice on surface–atmosphere system. The model demonstrates the potential the surface changed in response to eccentricity-driven changes importance of the solid-state phase transition between -N2 and in insolation. The subsequent discovery that N2 ice is much -N2, and the accompanying change in emissivity, for predicting more abundant on Pluto than CH4 ice (Owen et al. 1993) means the seasonal bulk of Pluto’s (and Triton’s) atmosphere. Specifically, that Pluto’s atmosphere is dominated by N2 (its vapor pressure is the model shows that under simplified but not unreasonable as- 4 '10 times larger than that of CH4 at Pluto temperatures (Brown sumptions Pluto may have nearly the same atmospheric pressure and Ziegler 1979)), but does not change the expectation of sea- at aphelion as it does now, near perihelion. The emissivity change sonally induced pressure oscillations, because N will also form which accompanies the – phase change should be included in 2 the next generation of Pluto and Triton seasonal models for the a vapor-pressure atmosphere. purposes of understanding the evolution of their atmospheres over Observations pertaining to the pressure of Pluto’s atmosphere seasonal and climatic timescales. c 1999 Academic Press and the temperature of its N2 ice are consistent with vapor- Key Words: Pluto; Pluto, atmosphere; Pluto, surface; Triton; pressure equilibrium. A stellar occultation by Pluto in 1988 atmospheres, evolution. set a lower limit on the perihelion surface pressure of 3 bar (Elliot et al. 1989, Hubbard et al. 1989, Elliot and Young 1992, Millis et al. 1993). Stansberry et al. (1994) argued that INTRODUCTION the occultation may not have reached Pluto’s surface, and that Pluto posesses a deep (50 km) troposphere. This hypothe- Pluto’s orbital eccentricity (0.25) means that it recieves 2.8 sis, strengthened by recent results indicating that Triton’s at- times as much sunlight at perihelion (which occurred in 1989) mosphere may now posess a troposphere approximately 50 km as it does at aphelion. The idea that this extreme insolation varia- deep (Elliot et al. 1999) implies that the true surface pressure of tion might lead to extreme changes in the bulk of the atmosphere N2 on Pluto is nearer 19 bar. Tryka et al. (1993) also argued followed close on the heels of the realization that Pluto posesses for a higher surface pressure, near 60 bar, on the basis of the an atmosphere. Cruikshank et al. (1976) discovered absorption observed shape of the N2 ice absorption feature. These pressures features in Pluto’s near-IR spectrum which were eventually at- correspond to the vapor pressure of N2 over a temperature range tributed to the presence of CH4 ice (Cruikshank and Apt 1984). of 35–40 K (Brown and Ziegler 1979). This is in excellent agree- Although the observed spectrum was due solely to absorption ment with temperatures calculated on the basis of surface en- by ice, it meant that Pluto had at least a tenuous CH4 atmo- ergy balance (Stansberry et al. 1994), and is not inconsistent with sphere because CH4 has a significant (0.1–100 bar) vapor pres- temperatures derived from far-IR observations of emission from sure at temperatures then predicted for Pluto (Cruikshank and Pluto (Altenhoff et al. 1988, Jewitt 1994, Stern et al. 1993, Tryka Silvaggio 1979, Trafton 1980). Stern and Trafton (1984) pointed et al. 1994, Spencer et al. 1997). Phase equilibrium is usually encountered in systems consid-

1 erably smaller than the entire surface–atmosphere interface of Current address: Steward Observatory, University of Arizona, 933 N. a planet (although Triton is another example of such a situ- Cherry Avenue, Tucson, AZ 85721. 2 Current address: Department of Physics and Astronomy, Northern Arizona ation). Despite the large scale of this system, the conditions University, Flagstaff, AZ 86011. of vapor–solid phase equilibrium, namely a single pressure and

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0019-1035/99 $30.00 Copyright c 1999 by Academic Press All rights of reproduction in any form reserved. 300 STANSBERRY AND YELLE temperature, have been theoretically shown to apply to the entire The term is the ratio of the total area of the N2 ice to its cross- ice–atmosphere interface (Leighton and Murray 1966, Trafton sectional area as viewed from the Sun; i.e., it is the ratio of the 1984, Yelle et al. 1995). Thus, a variety of observations and the- area over which thermal reradiation from the ice occurs to the ory are consistent with the idea that Pluto’s near-perihelion atmo- area receiving sunlight. sphere is in equilibrium with the surface N2 ice. We note that the We wish to use these relations to predict the seasonal vari- dual-volatile seasonal model of Trafton (1990) leads to atmo- ability of the temperature of Pluto’s N2 ice, and thereby the at- spheric pressures of N2 considerably lower than those derived mospheric pressure. In order to do so we must know the values from the single-volatile considerations above, and that the of the albedo, emissivity, and as a function of time. Volatile Trafton model gives results consistent with a 3-bar surface tranport models have been used to predict the distribution of pressure for Pluto (Trafton et al. 1998). That model is also of in- N2 ice, i.e., , as a function of time under the assumption of terest because, like the model we present here, it predicts that un- constant frost albedo and emissivity (Spencer 1990; Stansberry der certain conditions Pluto’s atmosphere may not freeze out at et al. 1990; Hansen and Paige 1992, 1996; Brown and Kirk aphelion. However, the other dual-volatile model for Triton and 1994). In general these models do a poor job of both explain- Pluto (Stansberry et al. 1996b, Trafton et al. 1998) comes to dif- ing the observed albedo patterns on Triton and predicting the ferent conclusions, so for current purposes we will assume that changes in atmospheric pressure which have now been detected single-phase vapor-pressure equilibrium is an adequate para- on Triton (Elliot et al. 1997, 1998). There is no reason to expect digm for exploring the seasonal evolution of Pluto’s atmospheric them to perform better on Pluto. Because our primary interest in pressure. this study is to examine the effect of emissivity on the seasonal frost temperature, and because existing volatile transport mod- THERMAL MODEL els are of limited utility in predicting the time behavior of ,we simply take = 4 in our models, equivalent to assuming that the Nitrogen ice everywhere on the surface of Pluto is at the entire planet is covered by N2 ice. Later we discuss how changes same temperature because sublimation, atmospheric transport, in due to volatile transport would influence our results. We fur- and condensation act to efficiently redistribute energy across the ther assume that N2 ice has a bolometric albedo of 0.8, based globe (e.g., Spencer et al. 1997 and references therein). The usual on Voyager imaging results from Triton (Stansberry et al. 1990) equation for the diurnally averaged equilibrium temperaure of and mutual event albedo maps of Pluto (Stansberry et al. 1994). the surface, as a function of latitude (), The detailed emissivity behavior of the N2 is discussed below. As noted above, Eqs. (1)–(3) are only applicable if the condi- Z 1 T 4 = , tion of frost isothermality is satisfied. The amount of latent heat Teq( ) S0(1 A) d cos (1) T that can be transported around the globe by winds of a given velocity dependens upon the atmospheric density: as the atmo- where is the emissivity of the ice, is the Stefan–Boltzmann spheric pressure falls, winds will grow stronger. When the wind constant, Teq is the radiative equilibrium temperature of the sur- speed begins to approach the sound speed, significant pressure face, S0 is the solar flux at Pluto, A is the bolometric albedo of gradients will be required to drive the flow (Trafton and Stern the ice (which we set to 0.8), is longitude, T is the longi- 1983, Yelle et al. 1995). The presence of significant pressure tude of the terminator at a given latitude, and is the local solar differences in the atmosphere implies temperature differences zenith angle, must be modified to account for the latent heat flux between different regions of N2 ice on the surface with which in the equation of local energy balance. Writing the cossine of the atmosphere is in contact; i.e., the condition of isothermal- the diurnally averaged solar zenith angle (the integral in Eq. (1)) ity is violated. Spencer et al. (1997) show that the condition of as ¯ gives isothermality breaks down when the N2 ice temperature falls below about 31 K, with a corresponding atmospheric pressure S ¯ (1 A) = T 4 + Lm˙ , (2) 0 of 0.1 bar. where L is the latent heat of sublimation per unit mass of N2 9 1 (2.6 10 erg/g ) (Brown and Ziegler 1979), and m˙ is the sub- EMISSIVITY AND THE – PHASE TRANSITION limation mass flux. For current conditions on Pluto the temperature of the N2 is the same everywhere to within a small fraction The N2 – solid phase transition occurs at T = 35.6 K, of a Kelvin (Yelle et al. 1995, Spencer et al. 1997). The N2 tem- where the vapor pressure is 4.2 bar (Brown and Ziegler 1979). perature can be found by integrating Eq. (2) over all of the the N2 N2 , the high-temperature phase, posesses a hexagonal crystal deposits on the surface and applying the constraint that the glo- structure in which the molecular orientations are disordered, bally averaged latent heat flux (Lm˙ ) is zero. This yields the while N2 , the low-temperature phase, posesses a cubic crystal globally constant temperature of the N2 ice as structure in which the molecules are highly ordered (Scott 1976). N is characterized by broad, weak absorption bands both in the 1/4 2 = S0(1 A) . near and the far infrared, while N is characterized by narrow, TN2 (3) 2 weak absorption bands in both spectral regions (St. Louis and FATE OF PLUTO’S ATMOSPHERE 301

TABLE I

N2 ice albedo 0.8 N2 emissivity 0.3 N2 emissivity 0.75 Solar constant 1587 erg cm2 s1 (@29.58 AU)

tuation and found that phase-transition “fronts” propagated into and out of the subsurface in response. Their model accounted for the latent heat of the – phase change (4% of the latent heat for the solid-to-vapor transition (Brown and Ziegler 1979); however, note that the expressions for the latent heat in that paper are incorrect: latent heats must be calculated using the vapor pressure relations and the Clausius–Clapeyron equation), but because the surface temperature variation was imposed and because they did not examine the global energy balance of the , FIG. 1. The absorbtion coefficients of , and liquid N2 in the far-IR. N2 ice along with its phase, their model has no predictive ability The heavy solid lines show the analytical approximations of the absorption data for the seasonal behavior of N2 and N2 . used in computing the emissivities used in this paper. Reproduced from Fig. 1 No Pluto or Triton seasonal study has accounted for the dif- of Stansberry et al. (1996a) with permission from Elsevier Science. ferent optical properties of N2 and N2 in the thermal infrared. Their weak absorption bands in this spectral region (20–400 m) Schnepp 1969). Figure 1 shows the far-IR absortion coefficients means that they will have low emissivities. Figure 2 shows the for the two solid phases and liquid N2. Since T is well above bolometric emissivities of N2 ice computed using Hapke theory the temperature where N2 ice isothermality is expected to break (Hapke 1993) and the data in Fig. 1 (Stansberry et al. 1996a). down (31K), the above thermal model is appropriate for studying N2 grain sizes on Pluto (and Triton) are thought to be in the seasonal effects of the – phase change. range 0.1–1 cm, determined from near-IR spectral modeling Duxbury and Brown (1993) investigated the seasonal stability (Cruikshank et al. 1993; Owen et al. 1993; Grundy et al. 1993; of N2 and N2 , as a function of depth, at two selected latitudes on Tryka et al. 1993, 1994). From Fig. 2, the bolometric emissivity Triton’s polar caps. They prescribed a surface temperature fluc- of a surface composed of grains in this size range is 0.11–0.30 = . = . (N2 ) and 0.40–0.85 (N2 ). Here we adopt 0 3 and 0 75 as our nominal emissivities for the two phases. As will be seen below, the value of determines the pressure we predict for the perihelion atmosphere and the timing of the onset of formation of the phase. The value of determines the temperature of Pluto’s N2 ice when overall absorbed insolation is low, and so is more important for determining the fate of Pluto’s atmosphere at aphelion. Our nominal value for is intentionally biased toward the upper end of the range in Fig. 2, so we predict an aphelion temperature and atmospheric pressure somewhat lower than those we would obtain if we used a more central value, such as 0.2. As discussed in detail by Stansberry et al. (1996a), con- taminants such as CH4 or its photolysis products may slightly increase , so in effect we are allowing for some contamina- tion of the N2 ice by choosing = 0.3. The nominal values we assume for the quantities in Eqs. (1)–(3) are summarized in Table I.

EMISSIVITY AND SEASONAL BEHAVIOR FIG. 2. The Planck-mean bolometric emissivity of N2 ice as a function of temperature and particle size. The double vertical line marks the – phase The sudden change in the emissivity of N2 at T has inter- transition temperature at 35.6 K. The dotted lines show the emissivity for nominal grain sizes deduced from visible and near-IR spectroscopy of Pluto and Triton. esting implications which can be illustrated by considering the Reproduced from Fig. 3 of Stansberry et al. (1996a) with permission from idealized case of N2 ice in radiative equilibrium with sunlight. Elsevier Science. Assuming that 50 erg cm 2 s 1 of solar radiation is absorbed by 302 STANSBERRY AND YELLE

How can Pluto’s climatic system satisfy the dual constraints of global energy balance and phase equilibirum between the gas and two solid phases of N2? Figure 4 shows the equilibrium temperature of N2 and N2 as a function of latitude approximately 40 years after perihelion. Pluto’s surface can be broken up into three different zones. Where the local diurnally averaged equilibrium temperature, Teq, is greater than T ,N2 is the stable phase, and it is subliming. Where Teq is less than T ,N2 is the stable phase, and it is condensing from the atmosphere. In these two zones (- and -stable) the fluxes of latent heat adjust the local ice temperature from Teq to T . Within the third region of Fig. 4 (between the vertical dotted lines) T is greater than eq T , and Teq is less than T . We now consider how the physical state of the N2 ice within this region can evolve in order to achieve an emissivity that satisfies the global constraint that = TN2 T . The physical state and evolution of the N2 ice within the re- FIG. 3. Pluto’s globally averaged equilibrium temperature as a function gion where neither N nor N is stable depends upon the rel- of time past perihelion passage or absorbed insolation. Insolation decreases as 2 2 Pluto recedes from the Sun, but the equilibrium temperature remains constant ative timescales for sublimation and solid-state conversion be- at the solid-N2 -to- transition temperature, 35.6 K, because of the emissivity tween the and phases. If solid-state conversion happens contrast between the two phases. more quickly, the phase composition of the ice will be able to readily adjust itself to local energy balance requirements. If sublimation happens more quickly, the molecules of the solid will the ice (appropriate for Pluto’s surface 40 years past perihe- not have time to rearrange themselves into the preferred solid lion), that the emissivities of N2 and N2 are as above, and that phase in response to changes in local energy balance (this might the ice is in its phase, we find that its equilibrium temperature result in the formation of layers of N and N ). We believe that = 2 2 is Teq 43 K, well above T : the ice cannot be in the phase. the solid-state phase change will be the preferred mode of evo- Computing the equilibrium temperature under the assumption lution for two reasons. First, the latent heat of the solid state = that the ice is in its phase, we find Teq 33 K, which is well phase change in only 4% of that associated with the solid-to- below T . We are forced to conclude that for some values of vapor phase change: a given energy imbalance will drive the insolation there is no radiative equilibrium solution involving solid-state phase change 25 times more rapidly than it will drive either of the pure phases of N2 ice: N2 would be too warm to sublimation. Second, when the local equilbrium temperature is exist and N2 would be too cold. close to T , as it typically is during the time when the ice is first Figure 3 shows how these considerations apply to Pluto’s entire surface–atmosphere system under the condition of vapor- pressure equilibrium. The figure shows solutions to Eq. (3) for = and = . As for an isolated patch of N2 ice, there are values of the globally averaged insolation for which the ice can- > not all be in either the or the phase: TN2 T (Eq. (3)) if < we plug in and TN2 T if we use . This apparent conflict between thermal balance and phase equilibrium is resolved by allowing both N2 and N2 to be present on Pluto’s surface and in contact with the atmosphere. Then, so long as all three phases are present and the atmosphere is thick enough to be hydro- = static, the Gibs phase rule requires that TN2 T . When both solid phases are present, the globally averaged emissivity will lie somewhere between and , and will have the value which = satisfies TN2 T . As illustrated by the figure, this condition can persist for a large fraction of Pluto’s orbit and will pertain even at aphelion for the nominal emissivity, albedo, and values assumed in our model. The predicted aphelion atmospheric FIG. 4. Diurnally averaged equilibrium temperatures as a function of latitude on Pluto circa AD 2030, 40 years after the most recent perihelion passage. pressure in this case is 4.2 bar. If the emissivity of N2 were The pure and phases are thermodynamically stable in the regions indicated the same as that of N2 , at aphelion TN2 would instead be about by the vertical dotted lines and arrows. Between the vertical dotted lines neither 28 K, and the atmospheric pressure about 5 nbar. phase is stable, but a mixture of the two phases is. FATE OF PLUTO’S ATMOSPHERE 303 begining to transition from one phase to the other, the sublima- emissivity has potentially important implications for volatile tion rate will be very small (and the timescale correspondingly transport models. Because mixed-phase regions are able to at- large). The slowness of sublimation during this stage increases tain a state of thermal equilibrium with absorbed insolation, they the likelihood that the solid-state phase transformation domi- will not sublime nor will fresh ice condense onto them from the nates the evolution of the physical state of the N2 ice. atmosphere: volatile transport in these areas comes to a halt. The above arguments will not hold if there is significant ki- This could have the effect of stabilizing the N2 ice distribution. netic inhibition of the solid-state phase change. However, no Although we have not explored this issue in any detail so far, we strong kinetic effects have been observed in a variety of labora- do discuss some implications of it below. tory experiments involving passing samples of N2 ice through We have calculated the latitudinal extent of the N2 and N2 the phase transition temperature (W. M. Grundy, personal com- stability zones, and the extent of the mixed-phase zone, as a munication). Despite the lack of obvious kinetic effects in the function of time over one Pluto orbit. The calculation was not a laboratory setting, there is a finite energy penalty associated seasonal transport model; rather we have simply used the equa- with the initial formation of cubic N2 crystals within hexa- tions of energy balance (Eqs. (1)–(3)). The lack of measurements gonal N2 , and vice versa. This energy penalty will result in or calculations for the emissivity of an intimate mixture of - and some kinetic inhibition of the phase change, with the result that -N2 grains and a model for the sizes and numbers of grains of the two phases will be metastable over a small temperature range each phase that will form preclude us from accurately modeling surrounding T . When the temperature is within this metastable the exact phase composition within the mixed-phase zone. We range the two phases can exist in contact with one another, i.e., as have approximated a solution by assuming that the emissivity a mixture of grains. This conclusion is supported by the phase- of the surface in the mixed-phase zone is linearly dependent on diagram work of Prokhvatilov and Yantsevich (1983). The finite the fraction of each phase present. width (in temperature space) of the metastable zone means that Figure 5 shows the and stability zones and the mixed- the grains of the two phases can be at slightly different temper- phase zone as a function of the time past Pluto’s perihelion. atures. Shading indicates the mixing ratio of N2 in the ice. An obvious A mixture of grains of N2 and N2 will have an emissivity in- feature of the map is that N never completely disappears from 2 termediate between and , with its exact value depending on the surface. For our nominal a portion of Pluto’s surface is still the mixing ratio of the two phases in the solid and the grain sizes in the mixed-phase state at aphelion, with the temperature of the associated with each phase. Considering the energy balance of N2 pinned at T , and the atmospheric pressure equal to 4.2 bar. such a mixed solid we find that its phase composition will be At aphelion the maximum N2 mixing ratio, which occurs near driven toward a state such that its equilibrium temperature will Pluto’s equator, falls to 0.32. From Eq. (3) we find that some N2 be equal to T . If the solid is too rich (i.e., its emissivity is too will be present at aphelion so long as 0.31. If is greater close to ), it will have an equilibrium temperature greater than than 0.31, Pluto will experience a period around perihelion T , and in particular the grains will be at a temperature somewhere the atmosphere will no longer be buffered by the presence what higher (but metastable) than that of the grains. This will of both solid phases. If = 0.35, all of the N will disappear 87 drive a decrease in the number of the grains via the solid-state 2 years past perihelion, and the atmospheric pressure will begin phase transformation to the phase, simultaneously increasing to fall. However, for = 0.35 the perihelion temperature will the emissivity and absorbing a small amount of latent heat and be 34.6 K, implying an atmospheric pressure of 2.0 bar. This thereby lowering the equilibrium temperature till it is equal to is still well above the minimum pressure of 0.1 bar required T . Conversely, if the solid is too rich in , its emissivity will be for the atmosphere to be in hydrostatic equilibrium (Spencer high, and its equilbrium temperature below T . This will drive et al. 1997). If is as high as 0.5, the aphelion N temperat- a decrease in the number of the grains via the solid-state phase 2 ure will be 31.7 K, with a corresponding atmospheric pressure change to the phase, with a resultant decrease in emissivity of 0.19 bar, and Pluto’s atmosphere may not be hydrostatic. and simultaneous release of latent heat, thereby increasing the equilibrium temperature till it is equal to T . An alternative and DISCUSSION perhaps more likely configuration for the N2 and N2 is that of layers. Because N2 ice is so transparent in both the visible and The ability of the N2 – emissivity contrast to keep Pluto’s the far-IR, both deposition of sunlight and emission of thermal atmosphere from freezing out is subject to a number of caveats radiation will peak below the surface, probably at around a few due to the simplifying assumptions we have used in our model. If centimeters depth. If the depths of absorption and reradiation are one takes issue either with the measured absorption coefficients different, temperature gradients will form, and N2 and N2 will of N2 or with the application of Hapke’s theory of emission to tend to be vertically segregated. In this case emissivity adjust- the problem of emission from Pluto’s N2 ice (Stansberry et al. ment could occur through changes in the thickness of the layers 1996), then perhaps the emissivity contrast is suspect. Unfortu- rather than in the number of particles of either phase. nately it is difficult to prepare and measure either the reflectiv- The ability of the “mixed-phase” portions of the surface to at- ity or the emissivity of a large enough sample of N2 ice to di- tain equilibrium temperatures equal to T by changing their rectly determine its bolometric emissivity. In the absence of such 304 STANSBERRY AND YELLE

FIG. 5. The latitudinal distribution of -N2 on Pluto as a function of time: the brightest areas are pure -N2, the darkest pure -N2, and the shading indicates intermediate fractions of the phase mixed with the phase. The solid line shows the subsolar latitude as a function of time; the dashed lines show the limit of the unilluminated portion of the surface. measurements, we are forced to rely on the simpler measure- ing out. Ice metamorphism and volatile transport also probably ments of absorption coefficients and the use of radiative transfer have some impact on the albedo of the N2 ice, and we have ig- theory. nored these effects as have nearly all existing studies of seasonal Grain-size changes resulting from seasonal processes could effects on Pluto and Triton. have potentially important effects on the emissivity of both Another aspect of volatile transport that we have not modeled phases of N2, as could the nature of the solid-state phase change is its impact on the distribution of the surface ice and there- itself. As the N2 ice ages it is plausible that the grains become fore on the amount of sunlight the ice receives and on the area larger, and that the emissivity of older, coarse-grained surfaces over which it radiates thermally. We neglected modeling this will be correspondingly higher than that for younger surfaces aspect of the volatile transport largely because previous mod- (Fig. 2). However, the typical grain size is constrained by the els of seasonal transport have not convincingly reproduced the near-IR spectroscopic measurements, so the values we have used albedo, and presumably N2 ice, distribution on Triton or Pluto. should be approximately correct for the bulk of the visible N2 ice. We concluded that any results we obtained by including sea- It has also been suggested that N2 freezes out as a nongranular sonal transport in this study would be subject to greater, not or large-grained glaze (e.g., Hansen and Page 1992), and a model less, uncertainty as a result. We can explore the potential impact of sintering of N2 ice shows that glazes may form under certain of volatile transport on our model by considering a couple of deposition conditions (Eluszkiewicz 1991). Such a glaze would scenarios. The dependence of TN2 on the ice configuration is have a high emissivity (in Fig. 2 → 1 as the grain size becomes contained in the parameter of Eq. (3); for large values of arbitrarily large), and if it turns out that N2 preferentially freezes the ice is predominantly in poorly lit and/or unilluminated ar- out as a glaze or as very large grains, the emissivity contrast be- eas, and TN is low. For smaller values of the ice is at least 2 tween it and N2 could be reduced or possibly even reversed. If partially in sunlight, and TN2 is higher. Some endmember values so, the atmosphere would be unstable to freeze-out as has previ- of range from 4 (for an ice-covered body or, in fact, for many ously been predicted by others. On the other hand, N2 is denser other reasonable configurations of the surface ice) and 2 (for ice ∞ than N2 , and it is likely that when the – phase transition oc- only on the sunlit hemisphere) to values approaching (for all curs in the solid state the change in volume may damage grains of the ice in the unilluminated area of the body, e.g., if the N2 of N2 ice, resulting in a smaller grain size for N2 than what we ice layer is extremely thin and sublimes completely during the have assumed, and a correspondingly lower emissivity for it. summer). For a single patch of ice at the subsolar point, and no This would have the effect of enhancing the emissivity contrast other ice on the body, = 1. between the two phases, and would strengthen the conclusion It is unlikely that approaches 2 given the natural tendency that this contrast will tend to keep the atmosphere from freez- of the N2 ice to sublime and move into dark regions: this volatile FATE OF PLUTO’S ATMOSPHERE 305 transport will tend to favor values of >2. It is also improb- atmospheric pressure will always be larger than 1 bar, and that able that approaches ∞: this would require that Pluto’s N2 the atmosphere will remain in its hydrostatic state. layer is so thin that it sublimes entirely during the summer (or The effects we have discussed in this paper should also apply even during the daytime). A significant fraction of Pluto’s sun- to the thermal balance of Triton’s N2 ice. Wehave chosen to focus lit regions must be covered with N2 ice, else we would not see on Pluto because the eccentricity-induced insolation forcing is its absorption bands in the reflectance spectrum (Owen et al. so much stronger than Triton’s obliquity-induced forcing that 1993, Grundy 1995, Grundy and Fink 1996). Also, if there is it is reasonable to expect other factors, such as the details of too little ice in the sunlit hemisphere the vapor pressure over the the ice distribution on the surface, to produce much smaller ice would currently be much lower than the atmospheric pres- perturbations to the basic conclusions than would be the case if sure, which is probably in the range 10–60 bar (Stansberry we had attempted to model Triton. Nonetheless, observations of et al. 1994, Tryka et al. 1994, Young 1994, Yelle and Elliot Triton and Pluto both offer the potential to test the hypotheses 1997, Young et al. 1999; although, cf. Elliot et al. 1989, Elliot presented here. and Young 1992, Millis et al. 1993, Trafton et al. 1998, Yelle and Elliot 1997). Also, Pluto, like Triton, tends to be brightest CONCLUSIONS in the hemisphere where insolation has been strongest over the past couple of decades (Spencer et al. 1997, Trafton et al. 1998, We have outlined a simplified model for studying the effect Young et al. 1999). The foregoing points regarding atmospheric of the N2 –N2 phase change, and the associated change in emis- pressure make it difficult to imagine that the well-illuminated sivity predicted by Stansberry et al. (1996a), on the seasonal high-albedo areas on Triton and Pluto are not repositories of N2 changes in Pluto’s atmospheric pressure. Under the assumption ice. In addition, low-albedo areas have fairly high equilibrium that volatile transport does not greatly affect the overall energy < . temperatures even when they are well away from the subsolar balance of the N2 ice ( 73 throughout the orbit) we show latitude, and N2 will preferentially sublime from them. While it that the emissivity contrast between the two phases calculated by is possible that some low-albedo areas do have some N2 ice on Stansberry et al. (1996a) will prevent Pluto’s atmosphere from them, this can only be true if the atmospheric pressure is high freezing out as Pluto recedes from the Sun. If volatile transport enough to stabilize the N2 there, again requiring the presence does largely denude Pluto’s subsolar regions of N2 ice as aphe- > of N2 ice in the well-illuminated high-albedo areas. Two addi- lion approaches ( 7.3) the atmosphere will freeze out, but the tional factors that argue against efficient removal of N2 ice from life of the atmosphere will still have been greatly prolonged by the sunlit portions of Pluto, especially near aphelion, are: (1) as the emissivity contrast. This conclusion is subject to uncertain- the insolation drops, more N2 ice will be deposited on the sur- ties related not only to volatile transport, but also relating to the face, tending to keep existing high-albedo, sunlit, volatile-ice evolution of other potentially important factors such as albedo, deposits from subliming, and (2) as discussed earlier, N2 in the grain size, and vertical stratification of the phases. Telescopic mixed-phase region may well become decoupled from the sea- observations of Triton and Pluto will be capable of detecting sonal transport, tending to create a volatile distribution more the phase of N2 ice only after significant amounts of it have static than that would exist otherwise. formed because it will tend to be present mostly in poorly lit or The above reasoning bolsters the supposition that volatile ice unilluminated portions of the surface. In situ spacecraft obser- deposits will probably be widespread in the sunlit regions of vations would be much more effective for detecting N2 early on. Pluto, and that will be larger than 2, but probably not much Stellar occultation and/or spacecraft measurements should allow greater than 4. A realistic upper limit on , representative of us to monitor Pluto’s atmospheric pressure in coming decades, the thermal balance if large portions of Pluto’s sunlit regions providing a direct test of the predictions of this model. More become denuded of N2 ice at some point in a seasonal cycle, detailed modeling is possible, and probably desireable, in view might be represented by setting = 8 in Eq. (3). Using this as- of the possibility of a spacecraft being sent to Pluto with the sumption we can estimate a plausible upper limit to the potential express intent of studying the neutral atmosphere. cooling effect of volatile transport on N2 ice energy balance over = . a seasonal cycle. Doing so we find that at aphelion TN2 29 1K, ACKNOWLEDGMENTS with a corresponding atmospheric pressure of 0.02 bar. This We thank Jonathan Lunine, John Spencer, and Will Grundy for their thoughtful is well below the values of TN2 and PN2 , 31 K and 0.1 bar, re- spectively (Yelle et al. 1995, Spencer et al. 1997), where Pluto’s input, and Larry Trafton and another reviewer for their suggestions. 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